$\begin{aligned} &f(x)=-2x^2-5x+1 \\\\ &h(x)=3(x+3)^2-11 \end{aligned}$ $h(f(-1))=$
Solution: When evaluating composite functions, we work our way inside out. To evaluate $h(f(-1))$, let's first evaluate $f(-1)$. Then we'll plug that result into $h$ to find our answer. Let's evaluate $f({-1})$. $\begin{aligned}f(x)&=-2x^2-5x+1\\\\ f({-1})&=-2({-1})^2-5({-1})+1~~~~~~~~~~\text{Plug in }x={-1}\\\\ &=-2+5+1\\\\ &={4}\end{aligned}$ We now know that $h(f({-1}))$ is the same as $h({4})$ because $f({-1}) = {4}$. Let's evaluate $h({4})$. $\begin{aligned}h(x)&=3(x+3)^2-11\\\\ h({{4}})&=3(({4})+3)^2- 11 ~~~~~~~~~~\text{Plug in }x={4}\\\\ &=3(7)^2-11\\\\ &=3(49)-11\\\\ &=136\end{aligned}$ The answer: $h(f(-1)) = 136$